In the pitcher of a blender, add some of the cooked soup in batches, filling only 1/2 – 2/3 full. Be careful not to overfill the blender with hot liquid, as the steam mixed with the swirling soup can spray out from the lid and burn. It’s best to cover the pitcher with its lid, and then use a kitchen towel to hold the lid. Starting on low speed, purée the soup until it’s mostly smooth and then increase the speed to high to create a super-fine purée. Pour this finished soup into a clean pot, fill the pitcher with the remaining soup and repeat the process. When all the soup is puréed, mix well and taste, and adjust the seasoning with salt or pepper as needed.